The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  1  1
 0 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2  0  0  0  0 X^2 X^3+X^2 X^2 X^3+X^2  0  0  0  0 X^2 X^3+X^2 X^2 X^2  0  0  0  0 X^2 X^3 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^3 X^3 X^3 X^2 X^2 X^3+X^2 X^3 X^3 X^3 X^3 X^2 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^3 X^3 X^3+X^2 X^2 X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^2 X^3 X^3 X^3+X^2 X^2  0 X^3  0  0 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2  0 X^2  0 X^2 X^3+X^2
 0  0 X^3+X^2  0 X^2 X^2 X^3+X^2  0  0  0 X^2 X^3+X^2 X^2 X^3+X^2  0  0 X^3 X^3 X^3+X^2 X^2 X^3+X^2 X^2 X^3 X^3 X^3 X^3 X^3+X^2 X^2 X^3+X^2  0 X^2 X^3 X^3 X^3 X^3 X^3 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3+X^2  0  0 X^2 X^2 X^2 X^2  0 X^3 X^3  0 X^3+X^2 X^3+X^2 X^3+X^2 X^2 X^3 X^3  0 X^3  0  0 X^2 X^2 X^2 X^3+X^2  0 X^3 X^2 X^3+X^2 X^2 X^2  0  0 X^2 X^3+X^2 X^2 X^3+X^2 X^3+X^2 X^2
 0  0  0 X^3+X^2 X^2  0 X^3+X^2 X^2 X^3 X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2 X^3 X^3 X^2 X^3+X^2  0  0 X^3+X^2 X^2  0  0 X^2 X^3+X^2 X^2 X^3+X^2 X^3  0 X^3+X^2 X^2 X^3 X^3 X^2  0 X^2 X^3 X^3+X^2  0 X^3+X^2 X^3 X^3+X^2 X^3 X^3 X^3+X^2 X^3+X^2  0 X^3 X^2 X^2  0  0 X^2 X^2  0 X^2 X^3  0 X^3+X^2  0 X^3+X^2 X^2  0  0 X^2 X^2 X^3  0 X^3+X^2 X^3  0  0 X^3

generates a code of length 79 over Z2[X]/(X^4) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+68x^76+24x^77+138x^78+592x^79+112x^80+24x^81+44x^82+18x^84+2x^86+1x^152

The gray image is a linear code over GF(2) with n=632, k=10 and d=304.
This code was found by Heurico 1.16 in 27.2 seconds.